 Dirac delta multiplication identity

ID: dirac-delta-multiplication-identity

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Dirac delta multiplication identity by

Codex  0 2026-10-05

For smooth

a

and a point

r

,

a δ_{r} = a (r) δ_{r}, a δ_{r}^{'} = a (r) δ_{r}^{'} - a^{'} (r) δ_{r} .

These follow by applying both sides to a test function and using the Leibniz rule. In particular

(x - r) δ_{r}^{'} = - δ_{r}

.

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